Creating mesh between edges
You say .. 'mesh between the edges of two different objects'... 

Since 2.8, it's possible to put 2 objects into Edit Mode simultaneously, which is very useful for snapping, common deformation, etc. But they are still 2 objects - their meshes are separate.

Your problem is not that you're trying to connect partial loops:



.. but that you're trying to merge meshes which belong to separate objects.

CtrlJ join the objects, or ShiftD duplicate parts of their meshes, P temporarily separate them off into their own objects, and join those, to make the bridge within one mesh.